Multiple solutions of a fourth-order nonhomogeneous equation with critical growth in R^4

Abstract

In this article we study the existence of at least two positive weak solutions of an nonhomogeneous fourth-order Navier boundary-value problem involving critical exponential growth on a bounded domain in $R^4$, with a parameter $\lambda >0$. We establish upper and lower bounds for $\lambda$, which determine multiplicity and non-existence of solutions.

Keywords

• Biharmonic
• critical exponent
• multiple solutions